Linearly unstable forced and free flow in an anisotropic porous channel

The combined forced and free convection flow in a horizontal porous channel saturated by a fluid is studied. The boundary walls are considered as uniformly heated-cooled with symmetric heat fluxes. The horizontal porous layer is modelled as anisotropic with different permeabilities in the horizontal and vertical directions. A fully-developed stationary flow in the porous channel exists, endowed with a temperature gradient inclined to the vertical. This basic stationary flow turns out to become linearly unstable when the Rayleigh number is sufficiently high, with a neutral stability condition strongly dependent on the P & eacute;clet number associated with the basic flow rate. A minimum P & eacute;clet number exists below which no linear instability arises. A streamfunction formulation is introduced to test the behaviour of the small-amplitude perturbations. The stability eigenvalue problem is solved numerically for different P & eacute;clet numbers and anisotropy ratios in order to evaluate the neutral stability threshold and the critical values for the onset of the linear instability.